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Highly Irregular Serial Correlation Tests

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Abstract

We develop tests for neglected serial correlation when the information matrix is repeatedly singular under the null. Specifically, we consider white noise against a multiplicative seasonal AR model, and a local-level model against a nesting UCARIMA one. Our proposals, which involve higher-order derivatives, are asymptotically equivalent to the likelihood ratio test but only require estimation under the null. Remarkably, we show that our proposed tests effectively check that certain autocorrelations of the observations are 0, so their asymptotic distribution is standard. We conduct Monte Carlo exercises that study their finite sample size and power properties, comparing them to alternative approaches.

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  • Dante Amengual & Xinyue Bei & Enrique Sentana, 2023. "Highly Irregular Serial Correlation Tests," Working Papers wp2023_2302, CEMFI.
    • Handle: RePEc:cmf:wpaper:wp2023_2302
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    More about this item

    Keywords

    Generalized extremum tests; higher-order identifiability; likelihood ratio test.;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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